Raoul Bott

Infobox Scientist
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name = Raoul Bott


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caption = Raoul Bott in 1986
birth_date = birth date|1923|9|24
birth_place = Budapest, Hungary
death_date = death date and age|2005|12|20|1923|9|24
death_place = San Diego, California
residence = SVK
USA
CAN
citizenship =
nationality =
ethnicity =
fields =
workplaces = University of Michigan in Ann Arbor
Harvard University
alma_mater = McGill University
Carnegie Mellon University
doctoral_advisor = Richard Duffin
academic_advisors =
doctoral_students = Stephen Smale
Lawrence Conlon
Daniel Quillen
Peter Landweber
Robert MacPherson
Robert Brooks
Robin Forman
Kevin Corlette
notable_students =
known_for =
author_abbrev_bot =
author_abbrev_zoo =
influences =
influenced =
awards = Oswald Veblen Prize in Geometry (1964)
Wolf Prize (2000)
religion =


footnotes =

Raoul Bott, FRS (born September 24 1923, died December 20 2005) was a mathematician known for numerous basic contributions to geometry in its broad sense.

He was born in Budapest, grew up in Slovakia, but spent his working life in the United States. His family emigrated to Canada in 1938, and subsequently he served in the Canadian Army in Europe during World War II. He later went to college at McGill University in Montreal, and then earned a Ph.D. from Carnegie Mellon University in Pittsburgh in 1949. His thesis, titled "Electrical Network Theory", was written under the direction of Richard Duffin. Afterward, he began teaching at the University of Michigan in Ann Arbor. He was a professor at Harvard University from 1959 to 1999, and received the Wolf Prize in 2000. In 2005, he was elected an Overseas Fellow of the Royal Society of London. He died in San Diego after a battle with cancer.

Initially he worked on the theory of electrical circuits (Bott-Duffin theorem from 1949), then switched to pure mathematics.

He studied the homotopy theory of Lie groups, using methods from Morse theory, leading to the Bott periodicity theorem (1956). In the course of this work, he introduced Morse-Bott functions, an important generalization of Morse functions.

This led to his role as collaborator over many years with Michael Atiyah, initially via the part played by periodicity in K-theory. Bott made important contributions towards the index theorem, especially in formulating related fixed-point theorems, in particular the so-called 'Woods Hole fixed-point theorem', a combination of the Riemann-Roch theorem and Lefschetz fixed-point theorem (it is named after Woods Hole, Massachusetts, the site of a conference at which collective discussion formulated it [http://www.whoi.edu/science/MPC/dept/meetings/atiyah_bott_35.html] ). The major Atiyah-Bott papers on what is now the Atiyah–Bott fixed-point theorem were written in the years up to 1968; they collaborated further in recovering in contemporary language results of Ivan Petrovsky on hyperbolic partial differential equations, prompted by Lars Gårding. In the 1980s, Atiyah and Bott investigated gauge theory, using the Yang-Mills equations on a Riemann surface to obtain topological information about the moduli spaces of stable bundles on Riemann surfaces.

He is also known in connection with the Borel-Bott-Weil theorem on representation theory of Lie groups via holomorphic sheaves and their cohomology groups; and for work on foliations.

In 1964, he was awarded the Oswald Veblen Prize in Geometry by the American Mathematical Society.

Bott had 20 Ph.D. students, including Stephen Smale, Lawrence Conlon, Daniel Quillen, Peter Landweber, Robert MacPherson, Robert Brooks, Robin Forman, and Kevin Corlette.

His mother and aunts spoke Hungarian. His Czech stepfather did not, so the principal language at home was German. He had an English governesses from a young age, so he also spoke perfect English (and retained a very faint English accent throughout his life). The language of his high school was Slovak. Despite all this Bott claimed a distaste for learning languages.

Publications

*Bott, Raoul Raoul Bott: collected papers. Vol. 4. Mathematics related to physics. Edited by Robert D. MacPherson. Contemporary Mathematicians. Birkhäuser Boston, Inc., Boston, MA, 1995. xx+485 pp. ISBN 0-8176-3648-X MR|1321890
* Bott, Raoul Raoul Bott: collected papers. Vol. 3. Foliations. Edited by Robert D. MacPherson. Contemporary Mathematicians. Birkhäuser Boston, Inc., Boston, MA, 1995. xxxii+610 pp. ISBN 0-8176-3647-1 MR|1321886
*Bott, Raoul Raoul Bott: collected papers. Vol. 2. Differential operators. Edited by Robert D. MacPherson. Contemporary Mathematicians. Birkhäuser Boston, Inc., Boston, MA, 1994. xxxiv+802 pp. ISBN 0-8176-3646-3MR|1290361
*Bott, Raoul Raoul Bott: collected papers. Vol. 1. Topology and Lie groups. Edited by Robert D. MacPherson. Contemporary Mathematicians. Birkhäuser Boston, Inc., Boston, MA, 1994. xii+584 pp. ISBN: 0-8176-3613-7 MR|1280032
*Bott, Raoul; Tu, Loring W. Differential forms in algebraic topology. Graduate Texts in Mathematics, 82. Springer-Verlag, New York-Berlin, 1982. xiv+331 pp. ISBN 0-387-90613-4 MR|0658304
*Bott, Raoul Lectures on K(X). Mathematics Lecture Note Series W. A. Benjamin, Inc., New York-Amsterdam 1969 x+203 pp.MR|0258020

External links

*MathGenealogy|id=7583
* [http://www.math.harvard.edu/history/bott/index.html Commemorative website at Harvard Math Department]
* [http://www.math.harvard.edu/history/bott/bottbio/index.html "The Life and Works of Raoul Bott"] , by Loring Tu
* [http://www.nytimes.com/2006/01/08/national/08bott.html "Raoul Bott, an Innovator in Mathematics, Dies at 82"] , "The New York Times", January 8, 2006

Persondata
NAME= Bott, Raoul
ALTERNATIVE NAMES=
SHORT DESCRIPTION=Hungarian-born mathematician
DATE OF BIRTH= 1923-9-24
PLACE OF BIRTH= Budapest, Hungary
DATE OF DEATH= 2005-12-20
PLACE OF DEATH= San Diego, California